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Introduction to Smooth Ergodic Theory

Luis Barreira Instituto Superior Técnico, Lisbon, Portugal
Yakov Pesin Pennsylvania State University, State College, PA
Available Formats:
Hardcover ISBN: 978-0-8218-9853-6
Product Code: GSM/148
277 pp
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-1-4704-0972-2 Product Code: GSM/148.E 277 pp List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Introduction to Smooth Ergodic Theory Luis Barreira Instituto Superior Técnico, Lisbon, Portugal Yakov Pesin Pennsylvania State University, State College, PA Available Formats:  Hardcover ISBN: 978-0-8218-9853-6 Product Code: GSM/148 277 pp  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-1-4704-0972-2 Product Code: GSM/148.E 277 pp
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$103.50
MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

Volume: 1482013
MSC: Primary 37;

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on the absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The authors also present a detailed description of all basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature.

This book is a revised and considerably expanded version of the previous book by the same authors Lyapunov Exponents and Smooth Ergodic Theory (University Lecture Series, Vol. 23, AMS, 2002). It is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wants to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. With more than 80 exercises, the book can be used as a primary textbook for an advanced course in smooth ergodic theory. The book is self-contained and only a basic knowledge of real analysis, measure theory, differential equations, and topology is required and, even so, the authors provide the reader with the necessary background definitions and results.

Graduate students interested in dynamical systems and ergodic theory and research mathematicians interested in smooth ergodic theory.

• Part 1. The core of the theory
• Chapter 1. Examples of hyperbolic dynamical systems
• Chapter 2. General theory of Lyapunov exponents
• Chapter 3. Lyapunov stability theory of nonautonomous equations
• Chapter 4. Elements of the nonuniform hyperbolicity theory
• Chapter 5. Cocycles over dynamical systems
• Chapter 6. The Multiplicative Ergodic Theorem
• Chapter 7. Local manifold theory
• Chapter 8. Absolute continuity of local manifolds
• Chapter 9. Ergodic properties of smooth hyperbolic measures
• Chapter 10. Geodesic flows on surfaces of nonpositive curvature
• Part 2. Selected advanced topics
• Chapter 11. Cone technics
• Chapter 12. Partially hyperbolic diffeomorphisms with nonzero exponents
• Chapter 13. More examples of dynamical systems with nonzero Lyapunov exponents
• Chapter 14. Anosov rigidity
• Chapter 15. $C^1$ pathological behavior: Pugh’s example

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Volume: 1482013
MSC: Primary 37;

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on the absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The authors also present a detailed description of all basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature.

This book is a revised and considerably expanded version of the previous book by the same authors Lyapunov Exponents and Smooth Ergodic Theory (University Lecture Series, Vol. 23, AMS, 2002). It is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wants to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. With more than 80 exercises, the book can be used as a primary textbook for an advanced course in smooth ergodic theory. The book is self-contained and only a basic knowledge of real analysis, measure theory, differential equations, and topology is required and, even so, the authors provide the reader with the necessary background definitions and results.

Graduate students interested in dynamical systems and ergodic theory and research mathematicians interested in smooth ergodic theory.

• Part 1. The core of the theory
• Chapter 1. Examples of hyperbolic dynamical systems
• Chapter 2. General theory of Lyapunov exponents
• Chapter 3. Lyapunov stability theory of nonautonomous equations
• Chapter 4. Elements of the nonuniform hyperbolicity theory
• Chapter 5. Cocycles over dynamical systems
• Chapter 6. The Multiplicative Ergodic Theorem
• Chapter 7. Local manifold theory
• Chapter 8. Absolute continuity of local manifolds
• Chapter 9. Ergodic properties of smooth hyperbolic measures
• Chapter 10. Geodesic flows on surfaces of nonpositive curvature
• Part 2. Selected advanced topics
• Chapter 11. Cone technics
• Chapter 12. Partially hyperbolic diffeomorphisms with nonzero exponents
• Chapter 13. More examples of dynamical systems with nonzero Lyapunov exponents
• Chapter 14. Anosov rigidity
• Chapter 15. $C^1$ pathological behavior: Pugh’s example
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